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The position of a particle in rectilinear motion is given by the equation (x = t3 - 2t2 + 10t - 4), where x is in meters and t is in seconds. What will be the velocity of the particle at 3s?
- a)20 m/s
- b)25 m/s
- c)15 m/s
- d)30 m/s
Correct answer is option 'B'. Can you explain this answer?
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Verified Answer
The position of a particle in rectilinear motion is given by the equat...
Position (x) = t3 – 2t2 + 10t – 4
Velocity (v) = 
At t = 3 s
V = 3 × 32 – 4 × 3 + 10 = 25 m/s
Most Upvoted Answer
The position of a particle in rectilinear motion is given by the equat...
Given:
x = t3 - 2t2 + 10t - 4 (position equation)
t = 3s (time at which velocity is to be found)
To find:
Velocity of the particle at t = 3s
Solution:
To find the velocity of the particle, we need to differentiate the given position equation with respect to time (t).
v = dx/dt (velocity equation)
where v is the velocity of the particle and dx/dt is the derivative of position equation with respect to time.
Differentiating the given position equation with respect to time (t), we get:
dx/dt = 3t2 - 4t + 10 (velocity equation)
Substituting t = 3s in the velocity equation, we get:
v = 3(3)2 - 4(3) + 10
v = 27 - 12 + 10
v = 25 m/s
Therefore, the velocity of the particle at t = 3s is 25 m/s.
Answer: Option B. 25 m/s.
x = t3 - 2t2 + 10t - 4 (position equation)
t = 3s (time at which velocity is to be found)
To find:
Velocity of the particle at t = 3s
Solution:
To find the velocity of the particle, we need to differentiate the given position equation with respect to time (t).
v = dx/dt (velocity equation)
where v is the velocity of the particle and dx/dt is the derivative of position equation with respect to time.
Differentiating the given position equation with respect to time (t), we get:
dx/dt = 3t2 - 4t + 10 (velocity equation)
Substituting t = 3s in the velocity equation, we get:
v = 3(3)2 - 4(3) + 10
v = 27 - 12 + 10
v = 25 m/s
Therefore, the velocity of the particle at t = 3s is 25 m/s.
Answer: Option B. 25 m/s.
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Community Answer
The position of a particle in rectilinear motion is given by the equat...
The position of a particle in rectilinear motion is defined by the relationship x=t3
-2t2+10t-6, where
x is in metres and t is in seconds determine (i) particle’s position, velocity and acceleration at
t=3secs (ii)average velocity during t=2seconds and t=3seconds(iii)average acceleration during
t=2seconds and t=3seconds.
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